Question

what other information is needed to prove that △abc ≅ △qrs by asa congruence theorem? (1 point)
(overline{ab}congoverline{qr})
(overline{bc}congoverline{rs})
(angle ccongangle s)
(overline{ac}congoverline{qs})

Explanation:

Step1: Recall ASA congruence theorem

The ASA (Angle - Side - Angle) congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Identify given angles

In \(\triangle ABC\) and \(\triangle QRS\), we can observe some pairs of angles are marked as congruent. We need the included side between the two pairs of congruent angles to be congruent.

Step3: Determine the included side

The included side between the angles for the ASA criterion for \(\triangle ABC\) and \(\triangle QRS\) is \(AB\) and \(QR\) respectively. For \(\triangle ABC\cong\triangle QRS\) by ASA, we need \(\overline{AB}\cong\overline{QR}\).

Answer:

\(\overline{AB}\cong\overline{QR}\) (the first option)